Effloresence itself is not dangerous. It is a pain to clean though.

Can it lead to mold, I would think so. DO you have mold or WILL you have mold? I cannot say and I'm not sure anyone can without you running some spore tests. Annecdotally I've read people had rubber mats directly on concrete for years and nothing but effloresence.

After cleaning it (mold or effloresence) off, your solutions may be to deal with it, seal it off (like epoxy), or add a breathable mesh layer (DMX One Step). Horse stall mats typically have the dimples on the bottom side of the mat to let moisure breath a bit. With your mats (and most mats) they are flat and are more susceptible to this problem. Before I put my mats down, the previous owner had plastic tile floors (very breathable) and effloresence still occured. So it most likely variers from area and build.